1) (3-4sin x) (3+4 cos x) = 0
9 - 12sin x + 9 cos x - 16sin x cos x = 0
9 - 12sin x + 9 cos x - 8sin 2x = 0
9 - 12sin x + 9 cos x - 16(1 - cos 2x) = 0
9 - 12sin x + 9 cos x - 16 + 16cos 2x = 0
-12sin x + 9 cos x + 16cos 2x - 7 = 0

2) (tg x + 3(tg x + 1) = 0
tg x + 3tg x + 3 = 0
4tg x + 3 = 0
tg x = -3/4

3) sin 2x = 3sin x cos^2 x
2sin x cos x = 3sin x cos^2 x
2 = 3cos x
cos x = 2/3
x = arccos(2/3)

4) sin 4x = sin 2x
2sin 2x cos 2x = 2sin x cos x
4sin x cos x(2cos^2 x - 1) = 2sin x cos x
8cos^2 x - 4 = 1
8cos^2 x = 5
cos x = sqrt(5)/4
x = arccos(sqrt(5)/4)